Structure of some categories of representations of infinite-dimensional lie algebras
Structure of some categories of representations of infinite-dimensional lie algebras
复制标题
无限维李代数的某些类别表示的结构
DOI：
10.1016/s0001-8708(82)80014-5
复制
发表时间：
1982
影响因子：
1.7
通讯作者：
V. Kac
中科院分区：
文献类型：
--
作者：
Vinay V. Deodhar;O. Gabber;V. Kac
有限维复半单李代数9的最高权表示在过去几年中得到了广泛的研究，并得到了许多有趣的结果（广泛的参考文献在[7]中给出）。在[2，3]中，引入了g的表示的类别cY，这被证明是考虑关于最高权重表示的各种问题的适当设置。本文的目的是将这一概念的研究推广到Kac-Moody代数，或者更一般地，推广到C上方阵A对应的逆李代数G（A）。这种代数的研究开始独立于[8，14]，随后证明了一些有趣的结果。这些结果表明，许多重要的性质，从有限维设置（即从上下文9）可以证明在一般设置涉及G（A）。特别地，范畴·的概念在[9]中被扩展到Kac-Moody代数的情况，并用于证明组合恒等式。
The highest weight representations of a finite-dimensional complex semisimple Lie algebra 9 have been studied extensively and a number of interesting results have been obtained in the last few years (an extensive bibliography is given in [7]). In [2, 3] a category cY of representations of g was introduced which turns out to be the proper setting for considering various questions regarding highest weight representations. The aim of this paper is to extend the study of this notion to a Kac-Moody algebra, or, more generally, to a contragredient Lie algebra G (A) corresponding to a square matrix A over C. The study of such algebras was begun independently in [8, 14] and subsequently a number of interesting results were proved. These results show that many important properties from the finite-dimensional setup (ie, from the context of 9) can be proved in the general setup involving G (A). In particular, the notion of category• was extended in [9] to the case of Kac-Moody algebras and used in the proof of combinatorial identities.